*Note: before reading this text, please read the article introducing the signature and weight of tilings.*
To enumerate the friezes in the plane, we'll begin with… a brief detour into three dimensions—to a cylinder! Imagine wrapping your strip—your favorite frieze—around a cylinder. Since antiquity, pottery and amphorae have been decorated around their circumference with charming motifs. These display rotational symmetry about the cylinder's axis, allowing a motif to be repeated all around the object. To pass from the cylinder to the plane, simply let the cylinder's radius tend to infinity.
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A little combinatorics
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